We study the Landau-Zener (LZ) dynamics in a setup of two Rydberg atoms with time-dependent detuning, both linear and periodic, using both the exact numerical calculations as well as the method of adiabatic impulse approximation (AIA). By varying the Rydberg-Rydberg interaction strengths, the system can emulate different three-level LZ models, for instance, bow-tie and triangular LZ models. The LZ dynamics exhibits non-trivial dependence on the initial state, the quench rate, and the interaction strengths. For large interaction strengths, the dynamics is well captured by AIA. In the end, we analyze the periodically driven case, and AIA reveals a rich phase structure involved in the dynamics. The latter may find applications in quantum state preparation, quantum phase gates, and atom interferometry.
A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the role of dissipation in the adiabatic following of the Hamiltonian eigenstates. Depending on the fact that the bare energies are equidistant or not, the relevant population transfer turns out to be very sensitive to the environmental interaction or relatively robust. The physical mechanisms on the basis of this behavior are discussed in detail.
We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.
Non-adiabatic transitions in multilevel systems appear in various fields of physics, but it is not easy to analyze their dynamics in general. In this paper, we propose to extend the adiabatic impulse approximation to multilevel systems. This approximation method is shown to be equivalent to a series of unitary evolutions and facilitates to evaluate the dynamics numerically. In particular, we analyze the dynamics of the Landau-Zener grid model and the multilevel Landau-Zener-Stückelberg-Majorana interference model, and confirm that the results are in good agreement with the exact dynamics evalu…
We study the motion of a cold atom in a frequency-modulated standing laser wave. If the detuning between the atomic electronic transition and the field is large, the atom moves in a modulated optical potential demonstrating known classical nonlinear effects such as chaos and nonlinear resonances. If the atom-field detuning is small, then two optical potentials emerge in the system, and the atom performs Landau-Zener (LZ) tunnelings between them. It is a radically non-classical behavior. However, we show that classical nonlinear structures in system's phase space (KAM-tori and chaotic layers) s…
The Landau-Zener model of a quantum mechanical two-level system driven with a linearly time dependent detuning has served over decades as a textbook paradigm of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2, 46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dyna…
We explore the asymmetric sequential Landau-Zener (LZ) dynamics in an ensemble of interacting Bose condensed two-level atoms coupled with a cavity field. Assuming the couplings between all atoms and the cavity field are identical, the interplay between atom-atom interaction and detuning may lead to a series of LZ transitions. Unlike the conventional sequential LZ transitions, which are symmetric to the zero detuning, the LZ transitions of Bose condensed atoms in a cavity field are asymmetric and sensitively depend on the photon number distribution of the cavity. In LZ processes involving singl…
In this paper I study the dynamics of a two-level atom interacting with a standing wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behaviour of the atomic motion is strongly affected d…
We irradiated an rf-SQUID qubit with large-amplitude and high frequency electromagnetic field. Population transitions between macroscopic distinctive quantum states due to Landau-Zener transitions at energy-level avoided crossings were observed. The qubit population on the excited states as a function of flux detuning and microwave power exhibits interference patterns. Some novel features are found in the interference and a model based on rate equations can well address the features.
We investigate the dynamics of a Bose--Einstein condensate (BEC) in a triple-well trap in a three-level approximation. The inter-atomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. New eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three level Landau-Zener model and the S…
We report the observation of multiple harmonic generation in electric dipole spin resonance in an InAs nanowire double quantum dot. The harmonics display a remarkable detuning dependence: near the interdot charge transition as many as eight harmonics are observed, while at large detunings we only observe the fundamental spin resonance condition. The detuning dependence indicates that the observed harmonics may be due to Landau-Zener transition dynamics at anticrossings in the energy level spectrum.
We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for $P$ for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a {\it perturbative} correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to appear for large couplings only, when $P$ is very small; this explains why the Landau-Zener model is often seen to provide more accurate results…
The rate of electron-positron pair production in linearly polarized counter-propagating lasers is evaluated from a recently discovered solution of the time-dependent Dirac equation. The latter is solved in momentum space where it is formally equivalent to the Schrödinger equation describing a strongly driven two-level system. The solution is found from a simple transformation of the Dirac equation and is given in compact form in terms of the doubly-confluent Heun's function. By using the analogy with the two-level system, it is shown that for high-intensity lasers, pair production occurs throu…
We study Landau-Zener-Stuckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from a LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also sho…
Single spin state evolution induced by the Landau-Zener-Stückelberg-Majorana (LZSM) interference in a Zeeman-spit four level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the Electric Dipole Spin Resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A nu…
In an earlier paper we have concluded that time-dependent parameters in atom-mode interaction can be utilized to modify the quantum field in a cavity. When an atom shoots through the cavity field, it is expected to experience a trigonometric time dependence of its coupling constant. We investigate the possibilities this offers to modify the field. As a point of comparison we use the solvable Rosen-Zener model, which has parameter dependencies roughly similar to the ones expected in a real cavity. We do confirm that by repeatedly sending atoms through the cavity, we can obtain filters on the ph…
The electron momentum density obtained from the Schwinger-like mechanism is evaluated for a graphene sample immersed in a homogeneous time-dependent electric field. Based on the analogy between graphene low-energy electrons and quantum electrodynamics (QED), numerical techniques borrowed from strong field QED are employed and compared to approximate analytical approaches. It is demonstrated that for some range of experimentally accessible parameters, the pair production proceeds by sequences of adiabatic evolutions followed by non-adiabatic Landau-Zener transitions, reminiscent of the Kibble-Z…
When the level separation of a qubit is modulated periodically across an avoided crossing, tunneling to the excited state - and consequently Landau-Zener-Stückelberg interference - can occur. The types of modulation studied so far correspond to a continuous change of the level separation. Here we study periodic latching modulation, in which the level separation is switched abruptly between two values and is kept constant otherwise. In this case, the conventional approach based on the asymptotic Landau-Zener (LZ) formula for transition probabilities is not applicable. We develop a novel adiabat…
Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics while completely suppressing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for three scenario…
A strong phase modulated coupling field leads to an amplitude modulation of a probe field in an electromagnetically induced transparency process. Time vs. detuning plots for different modulation frequencies reveals a transition between an adiabatic regime where a series of smooth pulses are created with a global phase dependent upon the detuning, and a non-adiabatic regime where a strong transient oscillating response is added to these pulses. In the extreme non-adiabatic regime, where the modulation frequency is higher than the transient decay time, a coherent interference pattern is revealed…
We study finite-time Landau-Zener transitions at a singlet-triplet level crossing in a GaAs double quantum dot, both experimentally and theoretically. Sweeps across the anticrossing in the high driving speed limit result in oscillations with a small visibility. Here we demonstrate how to increase the oscillation visibility while keeping sweep times shorter than T2* using a tailored pulse with a detuning dependent level velocity. Our results show an improvement of a factor ~2.9 for the oscillation visibility. In particular, we were able to obtain a visibility of ~0.5 for Stückelberg oscillation…
We study the dynamics of a nonlinear two-level crossing model with a cubic modification of the linear Landau-Zener diabatic energies. The solutions are expressed in terms of the bi-confluent Heun functions --- the generalization of the confluent hypergeometric functions. We express the finial transition probability as a convergent series of the parameters of the nonlinear laser detuning, and derive analytical approximations for the state populations in terms of parabolic cylinder and Whittaker functions. Tractable closed-form expressions are derived for a large part of the parameter space. We …
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with …
We explore the possibility to entangle an excitonic two-level system in a semiconductor quantum dot (QD) with a cavity defined on a photonic crystal by sweeping the cavity frequency across its resonance with the exciton transition. The dynamic cavity detuning is established by a radio frequency surface acoustic wave (SAW). It induces Landau-Zener (LZ) transitions between the excitonic and the photonic degrees of freedom and thereby creates a superposition state. We optimize this scheme by using tailored Fourier-synthesized SAW pulses with up to five harmonics. The theoretical study is performe…
Driven-Dissipative Dynamics of Measurement-Induced State Transitions
National Taiwan University（台湾大学）；National Tsing Hua University（清华大学）；National Center for Excellence in Quantum Information Science and Engineering, National Tsing Hua University（国家量子信息与工程卓越中心）；National Center for Theoretical Sciences（国家理论科学中心）
With silicon being the go-to material for spin qubits, and motivated by the demand of a scalable quantum computer architecture for fast and reliable quantum information transfer on-chip, we study coherent electron transport in a silicon double quantum dot. We first examine the valley-orbital dynamics in a silicon double dot, and discuss how to properly measure the tunnel couplings as well as the valley phase difference between two quantum dots. We then focus on possible phase and spin flip errors during spin transport across a silicon double dot. In particular, we clarify correction on the eff…
A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $π$ (i.e. a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $π$ pulse and an adiabatic chirped pulse, both of which produce complete population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman …
